Material characteristics are clearly important to a variety of magnetic analyses. Examples include the finite element analysis of an induction machine or in the magnetic equivalent circuit analysis of a power inductor. It may be argued that, in the case of power applications such as electric machinery and power converter inductors, the reluctance of flux paths is dominated by the air portions of the path during unsaturated conditions. However, under saturated conditions this is no longer true and the magnetic properties of the material become important.
In the design of power components, the usual case is that at least a portion of the magnetic material is under some degree of saturation. Otherwise, a less massive and less expensive component could have been designed. Thus the saturated or at least partially saturated case is a relevant one for design. This is particularly true when applying automated design procedures using population based design algorithms. In this case, many of the designs in the population will be at saturated operating points. Saturated conditions are also often encountered during transient analyses. For example, in an induction machine start up, large inrush currents saturate the stator teeth.
Although material manufacturers generally supply magnetic characteristics of the material they provide, they do not always provide the information for highly saturated conditions or for specific temperatures of interest. For these reasons, as well as for the purpose of validation of supplied data, it is often desirable to measure the magnetic characteristics.
Two common procedures for obtaining magnetic characteristics are Vibrating Sample Magnetometry (VSM) and IEEE Std. 393-1991.
Obtaining magnetic measurements using VSM requires extensive laboratory equipment, including the magnetometer itself and instruments for sample preparation. In addition, magnetic characterization of highly permeable materials (in particular ferromagnetic and ferrimagnetic materials) using VSM can result in significant inaccuracy because the error in the demagnetization factor that results from deviation from an ideal geometry increases with increasing permeability of the sample.
Alternately, the IEEE Standard for Test Procedures for Magnetic Cores, Vol., Iss., 10 Mar. 1992, hereby incorporated by reference, (IEEE Std. 393-1991) is a simple and relatively inexpensive procedure for characterizing a magnetic material using a toroidal sample. Since the flux forms closed paths while remaining inside the material, it is not necessary to consider demagnetization factors.
In order to determine the magnetic characteristics of a material in accordance with IEEE Std. 393-1991, a toroidal geometry is used with a primary winding and secondary coil, as shown in FIG. 1. Therein, ri and ro denote the inner and outer toroid radii, respectively; dt denotes the depth of the toroid into the page. The number of turns of the primary (excitation coil) and secondary (search coil) windings are denoted Np and Ns, respectively. The primary voltage and current are denoted vp and ip; the secondary voltage and current as vs and is.
An ac voltage waveform is applied to the primary winding, and Nc cycles of the primary current and secondary voltage waveforms are recorded. It is assumed that the secondary voltage probe has extremely high impedance so that the secondary current is effectively zero.
After carefully removing dc offsets in the measured primary current and secondary coil voltage, the magnetizing flux linking the secondary winding is calculated from Faraday's law:
                              λ          ⁡                      (            t            )                          =                                            ∫              0              t                        ⁢                                                            v                  s                                ⁡                                  (                  τ                  )                                            ⁢                                                          ⁢                              ⅆ                τ                                              +                      λ            ⁡                          (              0              )                                                          (        1        )            
Assuming there is no leakage flux, the flux density is uniformly distributed through the cross section of the material, and that the field intensity may be adequately determined by the mean path approximation, the field intensity and flux density is approximated as
                    H        =                                            N              p                        ⁢                          i              p                                            π            ⁡                          (                                                r                  o                                +                                  r                  i                                            )                                                          (        2        )                                B        =                  λ                                    N              s                        ⁢                                          d                t                            ⁡                              (                                                      r                    o                                    -                                      r                    i                                                  )                                                                        (        3        )            
In (2)-(3) B and H are assumed to be in the same (tangential) direction and thus vector notation is suppressed.
Two sources of error can result from the application of this procedure. First, the field intensity through a cross-section of the toroid is not uniformly distributed. Second, there is leakage flux associated with the primary winding, leading to distortions in the field distribution and localized saturation. Because of these effects, equation (3) underestimates the flux density produced by the coil. Both of these sources of error are accentuated during saturation.